We've been the first week in May, and it was awesome because of the reasons already listed.
Never been in January, but we did go in December 2014, and the weather was cold! Lows in the 40s, highs in the 50s. It was awesome. We didn't sweat. The entire trip was so pleasant and we loved wearing winter clothes at Disney. It was a real treat! The biggest downside is you have to pack more if you go in January, because it could be 85 or 55. My biggest issue with January is the refurbishments. You can have multiple attractions down.
You'll love early May!